🔷 При решении ноутбука используйте данный шаблон
✅ Можно добавлять новые ячейки любых типов
❌ Не нужно удалять текстовые ячейки c разметкой частей ноутбука и формулировками заданий
🔷 При оценивании задач учитывается код
✅ Задания, в которых необходим код, обычно помечаются фразами "Your code here"/"Ваш код" и аналогичными
❌ Ответы на вопросы без сопутствующего кода оцениваются в 0 баллов
❌ Наличе работоспособного кода в ноутбуке, если на сказано иного, обязательно
🔷 При оценивании задач учитываются выводы
✅ Задания, в которых необходимы выводы, обычно помечаются фразами Вывод"/"Ответ на вопрос"/"Ваш текст" и аналогичными
✅ Обычно выводы подразумевают под собой текстовый ответ (можно писать markdown, latex).
✅ Сопутствующие изображения, графики, таблички - приветствуются!
❌ При отсутствии выводов задание не засчитается на полный балл
В этом задании вы..:
**Примерное время выполнения (execution time/время выполнения, если нажать run all) всех ячеек ноутбука при правильной реализации: 60 минут **
Перед началом выполнения переведите ноутбук в Доверенный режим (Trusted) для корректного отображения изображений:
%config Completer.use_jedi = False
%load_ext autoreload
%autoreload 2
Сначала установим нужные нам версии библиотек. Мы гарантируем, что в данных версиях задание будет корректно отрабатывать.
После установки нужных версий, возможно, нужно перезагрузить среду (runtime), но скорее всего вам это не понадобится
На скачивание файла и установку понадобится не более 5 минут.
**Важно!**
Устанавливать нужные версии нужно каждый раз, когда создается новый рантайм. Например, если вы 2 часа подряд делаете это задание, то подготовить библиотеки достаточно 1 раз. Но если вы, например, начали в понедельник, затем закрыли/выключили ноутбук, то при продолжении в среду, вам нужно будет запустить рантайм заново и следовательно заново установить библиотеки.
**Важно!** Если вы предпочитаете делать практические задания на своем личном ноутбуке, то проверьте, что вы установили рабочее окружение в соответствии с гайдом.pdf)
**Важно!** В этом задании мы будем использовать полное виртуальное окружение, так как понадобятся библиотеки torch и tensorflow
Обратите внимание, что установка torch и tensorflow через pipможет сломать ваше окружение, особенно если вы используете GPU. Выполняйте их установку в соответствии с Вашей конфигурацией системы или в отдельном виртуальном окружении
# !!! Данный блок будет работать только в Google-Colab !!!
! gdown 19ZRLAdlNBI5OScrbxXzO3iaWJSkJlXeA
! pip install -r /content/requirements_2024_25_for_colab_full.txt
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Installing collected packages: pep8, triton, tqdm, pytest, pycodestyle, plotly, nvidia-nvtx-cu12, nvidia-nccl-cu12, nvidia-cusparse-cu12, nvidia-curand-cu12, nvidia-cufft-cu12, nvidia-cuda-runtime-cu12, nvidia-cuda-nvrtc-cu12, nvidia-cuda-cupti-cu12, nvidia-cublas-cu12, numpy, jedi, scipy, pandas, nvidia-cusolver-cu12, nvidia-cudnn-cu12, h5py, xgboost, torch, scikit-learn, scikit-image, matplotlib, lightgbm, keras, gdown, torchvision, seaborn, catboost, umap-learn, ipympl
Attempting uninstall: triton
Found existing installation: triton 3.2.0
Uninstalling triton-3.2.0:
Successfully uninstalled triton-3.2.0
Attempting uninstall: tqdm
Found existing installation: tqdm 4.67.1
Uninstalling tqdm-4.67.1:
Successfully uninstalled tqdm-4.67.1
Attempting uninstall: pytest
Found existing installation: pytest 8.3.5
Uninstalling pytest-8.3.5:
Successfully uninstalled pytest-8.3.5
Attempting uninstall: plotly
Found existing installation: plotly 5.24.1
Uninstalling plotly-5.24.1:
Successfully uninstalled plotly-5.24.1
Attempting uninstall: nvidia-nvtx-cu12
Found existing installation: nvidia-nvtx-cu12 12.4.127
Uninstalling nvidia-nvtx-cu12-12.4.127:
Successfully uninstalled nvidia-nvtx-cu12-12.4.127
Attempting uninstall: nvidia-nccl-cu12
Found existing installation: nvidia-nccl-cu12 2.21.5
Uninstalling nvidia-nccl-cu12-2.21.5:
Successfully uninstalled nvidia-nccl-cu12-2.21.5
Attempting uninstall: nvidia-cusparse-cu12
Found existing installation: nvidia-cusparse-cu12 12.5.1.3
Uninstalling nvidia-cusparse-cu12-12.5.1.3:
Successfully uninstalled nvidia-cusparse-cu12-12.5.1.3
Attempting uninstall: nvidia-curand-cu12
Found existing installation: nvidia-curand-cu12 10.3.6.82
Uninstalling nvidia-curand-cu12-10.3.6.82:
Successfully uninstalled nvidia-curand-cu12-10.3.6.82
Attempting uninstall: nvidia-cufft-cu12
Found existing installation: nvidia-cufft-cu12 11.2.3.61
Uninstalling nvidia-cufft-cu12-11.2.3.61:
Successfully uninstalled nvidia-cufft-cu12-11.2.3.61
Attempting uninstall: nvidia-cuda-runtime-cu12
Found existing installation: nvidia-cuda-runtime-cu12 12.5.82
Uninstalling nvidia-cuda-runtime-cu12-12.5.82:
Successfully uninstalled nvidia-cuda-runtime-cu12-12.5.82
Attempting uninstall: nvidia-cuda-nvrtc-cu12
Found existing installation: nvidia-cuda-nvrtc-cu12 12.5.82
Uninstalling nvidia-cuda-nvrtc-cu12-12.5.82:
Successfully uninstalled nvidia-cuda-nvrtc-cu12-12.5.82
Attempting uninstall: nvidia-cuda-cupti-cu12
Found existing installation: nvidia-cuda-cupti-cu12 12.5.82
Uninstalling nvidia-cuda-cupti-cu12-12.5.82:
Successfully uninstalled nvidia-cuda-cupti-cu12-12.5.82
Attempting uninstall: nvidia-cublas-cu12
Found existing installation: nvidia-cublas-cu12 12.5.3.2
Uninstalling nvidia-cublas-cu12-12.5.3.2:
Successfully uninstalled nvidia-cublas-cu12-12.5.3.2
Attempting uninstall: numpy
Found existing installation: numpy 2.0.2
Uninstalling numpy-2.0.2:
Successfully uninstalled numpy-2.0.2
Attempting uninstall: scipy
Found existing installation: scipy 1.14.1
Uninstalling scipy-1.14.1:
Successfully uninstalled scipy-1.14.1
Attempting uninstall: pandas
Found existing installation: pandas 2.2.2
Uninstalling pandas-2.2.2:
Successfully uninstalled pandas-2.2.2
Attempting uninstall: nvidia-cusolver-cu12
Found existing installation: nvidia-cusolver-cu12 11.6.3.83
Uninstalling nvidia-cusolver-cu12-11.6.3.83:
Successfully uninstalled nvidia-cusolver-cu12-11.6.3.83
Attempting uninstall: nvidia-cudnn-cu12
Found existing installation: nvidia-cudnn-cu12 9.3.0.75
Uninstalling nvidia-cudnn-cu12-9.3.0.75:
Successfully uninstalled nvidia-cudnn-cu12-9.3.0.75
Attempting uninstall: h5py
Found existing installation: h5py 3.13.0
Uninstalling h5py-3.13.0:
Successfully uninstalled h5py-3.13.0
Attempting uninstall: xgboost
Found existing installation: xgboost 2.1.4
Uninstalling xgboost-2.1.4:
Successfully uninstalled xgboost-2.1.4
Attempting uninstall: torch
Found existing installation: torch 2.6.0+cu124
Uninstalling torch-2.6.0+cu124:
Successfully uninstalled torch-2.6.0+cu124
Attempting uninstall: scikit-learn
Found existing installation: scikit-learn 1.6.1
Uninstalling scikit-learn-1.6.1:
Successfully uninstalled scikit-learn-1.6.1
Attempting uninstall: scikit-image
Found existing installation: scikit-image 0.25.2
Uninstalling scikit-image-0.25.2:
Successfully uninstalled scikit-image-0.25.2
Attempting uninstall: matplotlib
Found existing installation: matplotlib 3.10.0
Uninstalling matplotlib-3.10.0:
Successfully uninstalled matplotlib-3.10.0
Attempting uninstall: lightgbm
Found existing installation: lightgbm 4.5.0
Uninstalling lightgbm-4.5.0:
Successfully uninstalled lightgbm-4.5.0
Attempting uninstall: keras
Found existing installation: keras 3.8.0
Uninstalling keras-3.8.0:
Successfully uninstalled keras-3.8.0
Attempting uninstall: gdown
Found existing installation: gdown 5.2.0
Uninstalling gdown-5.2.0:
Successfully uninstalled gdown-5.2.0
Attempting uninstall: torchvision
Found existing installation: torchvision 0.21.0+cu124
Uninstalling torchvision-0.21.0+cu124:
Successfully uninstalled torchvision-0.21.0+cu124
Attempting uninstall: seaborn
Found existing installation: seaborn 0.13.2
Uninstalling seaborn-0.13.2:
Successfully uninstalled seaborn-0.13.2
Attempting uninstall: umap-learn
Found existing installation: umap-learn 0.5.7
Uninstalling umap-learn-0.5.7:
Successfully uninstalled umap-learn-0.5.7
ERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.
google-colab 1.0.0 requires pandas==2.2.2, but you have pandas 2.1.4 which is incompatible.
thinc 8.3.6 requires numpy<3.0.0,>=2.0.0, but you have numpy 1.26.4 which is incompatible.
mizani 0.13.3 requires pandas>=2.2.0, but you have pandas 2.1.4 which is incompatible.
plotnine 0.14.5 requires matplotlib>=3.8.0, but you have matplotlib 3.7.1 which is incompatible.
plotnine 0.14.5 requires pandas>=2.2.0, but you have pandas 2.1.4 which is incompatible.
torchaudio 2.6.0+cu124 requires torch==2.6.0, but you have torch 2.3.1 which is incompatible.
tensorflow 2.18.0 requires keras>=3.5.0, but you have keras 3.4.1 which is incompatible.
Successfully installed catboost-1.2.7 gdown-5.1.0 h5py-3.11.0 ipympl-0.9.4 jedi-0.19.2 keras-3.4.1 lightgbm-4.4.0 matplotlib-3.7.1 numpy-1.26.4 nvidia-cublas-cu12-12.1.3.1 nvidia-cuda-cupti-cu12-12.1.105 nvidia-cuda-nvrtc-cu12-12.1.105 nvidia-cuda-runtime-cu12-12.1.105 nvidia-cudnn-cu12-8.9.2.26 nvidia-cufft-cu12-11.0.2.54 nvidia-curand-cu12-10.3.2.106 nvidia-cusolver-cu12-11.4.5.107 nvidia-cusparse-cu12-12.1.0.106 nvidia-nccl-cu12-2.20.5 nvidia-nvtx-cu12-12.1.105 pandas-2.1.4 pep8-1.7.1 plotly-5.15.0 pycodestyle-2.12.1 pytest-7.4.4 scikit-image-0.23.2 scikit-learn-1.3.2 scipy-1.13.1 seaborn-0.13.1 torch-2.3.1 torchvision-0.18.1 tqdm-4.66.5 triton-2.3.1 umap-learn-0.5.6 xgboost-2.1.1
import catboost
assert(catboost.__version__ == '1.2.7')
Теперь можно приступать к выполнению задания! :)
В данной работе вам предстоит познакомится с методами машинного обучения без учителя — кластеризацией и алгоритмами снижения размерности.
Рекомендуется использовать Kaggle так как в нём корректно работают интерактивные визуализации.
Здесь перечислены основные функции и библиотеки, которые могут понадобиться Вам в процессе выполнения задания. Подключение других библиотек возможно, но нежелательно. Работа каких-либо других библиотек не гарантируется.
import os
import gdown
import scipy
import numpy as np
import tqdm.auto as tqdm
import matplotlib
import matplotlib.pyplot as plt
from matplotlib.offsetbox import OffsetImage, AnnotationBbox
from ipywidgets import interactive, fixed, interact_manual, IntSlider, FloatLogSlider, FloatSlider
import torch
from torchvision.datasets import CIFAR10
# Необходима преварительная установка tensorflow
from keras.applications.inception_v3 import InceptionV3, preprocess_input
import sklearn
from sklearn.decomposition import KernelPCA
from sklearn.cluster import KMeans, DBSCAN, AgglomerativeClustering
# Библиотека umap-learn, а не umap
from umap import UMAP
from sklearn.manifold import TSNE, Isomap
from sklearn.model_selection import train_test_split
from sklearn.datasets import make_classification, make_moons, make_blobs
from sklearn.preprocessing import StandardScaler, MinMaxScaler
from warnings import simplefilter
from sklearn.exceptions import ConvergenceWarning
simplefilter("ignore", category=ConvergenceWarning)
Определим вспомогательную функцию для отрисовки двумерных кластеризованных данных. При выполенении задания желательно пользоваться этой функцией для визуализации. При необходимости можете менять сигнатуру и поведение функции как вам удобно, оставляя стиль отрисовки в целом неизменным.
def plot_2d_data(data, labels, title='Исходные данные', cmap='tab20', ax=None):
'''
Отрисовка 2d scatter plot.
:param np.ndarray data: 2d массив точек
:param Union[list, np.ndarray] labels: список меток для каждой точки выборки
:param str title: Заголовок графика
:param str cmap: Цветовая палитра
:param ax Optional[matplotlib.axes.Axes]: Оси для отрисовки графика.
Если оси не заданы, то создаётся новая фигура и сразу же происходит её отрисовка
Иначе, график добавляется на существуюущие оси. Отрисовки фигуры не происходит
'''
n_clusters = len(np.unique(labels))
if ax is None:
fig, ax = plt.subplots(1, 1, figsize=(10, 5))
else:
fig = None
scatter = ax.scatter(
data[:, 0], data[:, 1], c=labels,
cmap=plt.get_cmap(cmap, n_clusters)
)
cbar = plt.colorbar(scatter, label='Номер кластера', ax=ax)
cbar.set_ticks(np.min(labels) + (np.arange(n_clusters) + 0.5) * (n_clusters - 1) / n_clusters)
cbar.set_ticklabels(np.unique(labels))
ax.set_title(title)
ax.grid(True)
if fig is not None:
fig.tight_layout()
plt.show()
Также используйте написанные реализации из [Base] задания:
def silhouette_score(x, labels):
'''
:param np.ndarray x: Непустой двумерный массив векторов-признаков
:param np.ndarray labels: Непустой одномерный массив меток объектов
:return float: Коэффициент силуэта для выборки x с метками labels
'''
# Ваш код здесь:\(º □ º l|l)/
unique_labels, label_counts = np.unique(labels, return_counts=True)
if len(unique_labels) == 1:
return 0.0
distances = sklearn.metrics.pairwise_distances(x)
n = len(labels)
# Precompute cluster indices and sizes
cluster_indices = {label: np.where(labels == label)[0] for label in unique_labels}
cluster_sizes = {label: len(indices) for label, indices in cluster_indices.items()}
# Precompute sum of distances for each cluster
sum_distances = {}
for label in unique_labels:
sum_distances[label] = distances[:, cluster_indices[label]].sum(axis=1)
total_silhouette = 0.0
for i in range(n):
label = labels[i]
cluster_size = cluster_sizes[label]
if cluster_size == 1:
continue
# Calculate s_i
s_i = (sum_distances[label][i] - distances[i, i]) / (cluster_size - 1)
# Calculate d_i
other_labels = [cur_label for cur_label in unique_labels if cur_label != label]
means = [
sum_distances[cur_label][i] / cluster_sizes[cur_label]
for cur_label in other_labels
]
d_i = np.min(means)
# Compute silhouette for current point
maxim = max(s_i, d_i)
sil_i = (d_i - s_i) / maxim if maxim != 0 else 0.0
total_silhouette += sil_i
return total_silhouette / n
def bcubed_score(true_labels, predicted_labels):
'''
:param np.ndarray true_labels: Непустой одномерный массив меток объектов
:param np.ndarray predicted_labels: Непустой одномерный массив меток объектов
:return float: B-Cubed для объектов с истинными метками true_labels и предсказанными метками predicted_labels
'''
# Ваш код здесь:\(º □ º l|l)/
same_true = true_labels[:, None] == true_labels
same_pred = predicted_labels[:, None] == predicted_labels
correctness = same_true & same_pred
correct_in_cluster = correctness.sum(axis=1)
pred_cluster_size = same_pred.sum(axis=1)
true_cluster_size = same_true.sum(axis=1)
precision = np.mean(correct_in_cluster / pred_cluster_size)
recall = np.mean(correct_in_cluster / true_cluster_size)
if (precision + recall) == 0:
return 0.0
return 2 * (precision * recall) / (precision + recall)
При выполнении задания запрещено:
При оформлении задания обратите внимание на форматирование кода и на оформление графиков:
Графики должны быть с одной стороны понятными и информативными, а с другой стороны красивыми. Вот несколько пунктов, которые помогут удовлетворить этим требования:
matplotlib_inline.backend_inline.set_matplotlib_formats('pdf', 'svg'). Если изображения в векторном формате приводят к слишком большому размеру Jupyter Notebook можете использовать растровые изображения с высоким dpi. Напирмер, можно установить глобальный dpi в matplotlib: matplotlib.rcParams['figure.dpi'] = 300title)log, symlog по необходимости[xy]ticks, [xy]ticklabels вручную. Подписи тиков на осях не должны сливаться как на одной оси, так и между нимиplt.style.use('seaborn-colorblind')
# Или
plt.style.use('tableau-colorblind10')
# Затем, при отрисовке графиков не используйте параметр cmap
Синтетические данные имеют достаточно простую структуру, поэтому методы снижения размерности позволяют получать хорошее низкоразмерное представление с достаточно выраженными кластерами. Однако, реальные данные могут быть устроены существенно сложнее. Посмотрим как поведут себя методы снижения размерности на датасете с картинками CIFAR10.
Загрузим датасет. Будем использовать только часть обучающей выборки, чтобы ускорить вычисления на высокоразмерных данных.
cifar10_test_dataset = CIFAR10('./cifar10', train=False, download=True)
cifar10_train_dataset = CIFAR10('./cifar10', train=True, download=False)
cifar10_labels_test = np.array(cifar10_test_dataset.targets)
cifar10_labels_train = np.array(cifar10_train_dataset.targets)
cifar10_images_test = cifar10_test_dataset.data
cifar10_images_train = cifar10_train_dataset.data
cifar10_images_train, _, cifar10_labels_train, _ = train_test_split(
cifar10_images_train, cifar10_labels_train,
train_size=cifar10_images_test.shape[0], stratify=cifar10_labels_train, random_state=6886
)
cifar10_data_test = (cifar10_images_test.astype(np.float32) / 255.0).reshape([cifar10_images_test.shape[0], -1])
cifar10_data_train = (cifar10_images_train.astype(np.float32) / 255.0).reshape([cifar10_images_train.shape[0], -1])
Downloading https://www.cs.toronto.edu/~kriz/cifar-10-python.tar.gz to ./cifar10/cifar-10-python.tar.gz
100%|██████████| 170498071/170498071 [00:01<00:00, 99240961.36it/s]
Extracting ./cifar10/cifar-10-python.tar.gz to ./cifar10
Отобразим данные в проекции на две случайные оси. Для удобства воспользуемся здесь ещё одним вариантом динамического контента в jupyter notebook — при наведении на точку на графике будем отображать исходную картинку.
def plot_interactive(lowd_data, images, labels, names, n_dots=1000, image_scale=1.0):
with matplotlib.rc_context(rc={
'font.size': image_scale * matplotlib.rcParams['font.size'],
'xtick.major.size': image_scale * matplotlib.rcParams['xtick.major.size'],
'xtick.minor.size': image_scale * matplotlib.rcParams['xtick.minor.size'],
'ytick.major.size': image_scale * matplotlib.rcParams['ytick.major.size'],
'ytick.minor.size': image_scale * matplotlib.rcParams['ytick.minor.size'],
'axes.linewidth': image_scale * matplotlib.rcParams['axes.linewidth'],
'grid.linewidth': image_scale * matplotlib.rcParams['grid.linewidth'],
'patch.linewidth': image_scale * matplotlib.rcParams['patch.linewidth'],
'xtick.major.width': image_scale * matplotlib.rcParams['xtick.major.width'],
'xtick.minor.width': image_scale * matplotlib.rcParams['xtick.minor.width'],
'ytick.major.width': image_scale * matplotlib.rcParams['ytick.major.width'],
'ytick.minor.width': image_scale * matplotlib.rcParams['ytick.minor.width'],
'lines.markeredgewidth': image_scale * matplotlib.rcParams['lines.markeredgewidth'],
}):
fig, ax = plt.subplots(1, 1, figsize=(image_scale * 10, image_scale * 5))
fig.set_dpi(300)
ax.grid(True)
n_clusters = len(np.unique(labels))
scatter = plt.scatter(
lowd_data[:n_dots, 0], lowd_data[:n_dots, 1], s=image_scale * 10,
c=labels[:n_dots], cmap=plt.get_cmap('tab20', n_clusters), edgecolors='none'
)
cbar = plt.colorbar(scatter, ax=ax, label='Название кластера')
cbar.set_ticks(np.min(labels[:n_dots]) + (np.arange(n_clusters) + 0.5) * (n_clusters - 1) / n_clusters)
cbar.set_ticklabels(names)
offset_image = OffsetImage(images[0], zoom=image_scale * 2.0)
ann_bbox = AnnotationBbox(
offset_image, (0,0), xybox=(image_scale * 50., image_scale * 50.), xycoords='data',
boxcoords="offset points", pad=0.3, arrowprops=dict(
arrowstyle='->, head_length={0:.2f}, head_width={1:.2f}'.format(
image_scale * 0.4, image_scale * 0.2
)
)
)
ax.add_artist(ann_bbox)
ax.set_title('Распределение данных CIFAR10 в проекции на 2 случайные оси')
ann_bbox.set_visible(False)
def image_hover(event):
if scatter.contains(event)[0]:
ind, *_ = scatter.contains(event)[1]["ind"]
w, h = fig.get_size_inches() * fig.dpi
ws = (event.x > w / 2.) * -1 + (event.x <= w / 2.)
hs = (event.y > h / 2.) * -1 + (event.y <= h / 2.)
ann_bbox.xybox = (image_scale * 50.0 * ws, image_scale * 50.0 * hs)
ann_bbox.set_visible(True)
ann_bbox.xy =(lowd_data[ind, 0], lowd_data[ind, 1])
offset_image.set_data(images[ind])
else:
ann_bbox.set_visible(False)
fig.canvas.draw_idle()
fig.canvas.mpl_connect('motion_notify_event', image_hover)
plt.show()
%matplotlib ipympl
matplotlib.rcParams['figure.dpi'] = 300
# Для работы в Google Colab нужно выполнить специфичную магию
# Обычно, она не срабатывает с первого раза, поэтому может потребоваться
# несколько раз выполнить ячейку и несколько раз попробовать нарисовать график
try:
from google.colab import output
output.enable_custom_widget_manager()
except:
pass
# Если картинка окажется слишком маленькой/большой, то поменяйте image_scale на подходящее значение
plot_interactive(
cifar10_data_train[:, [17, 64]], cifar10_images_train, cifar10_labels_train,
cifar10_test_dataset.classes, n_dots=2000, image_scale=0.35
)
Вернёмся в статичный режим отрисовки изображений:
%matplotlib inline
matplotlib.rcParams['figure.dpi'] = 300
</font>
Воспользуйтесь алгоритмами снижения размерности TSNE, UMAP, Isomap, KernelPCA для визуализации картинок.
Постройте визуализацию низкоразмерного представления, полученного с помощью этих моделей — изобразите четыре графика в одной строке. Во второй строке отобразите результат применения обученных моделей на тестовой выборке. Если для данного алгоритма невозможно сделать предсказания на тестовой выборке — оставьте соответствующий график пустым. Обозначьте разными цветами разные классы объектов. Для повышения производительности можете отобразить только часть выборки на графике ($1000\text{-}2000$ объектов).
**Замечание:** обратите внимание, что все алгоритмы снижения размерности также требуют правильного масштабирования признаков, для корректной работы и интерпретируемых результатов.
# Ваш код здесь:\(º □ º l|l)/
# t-SNE для обучающей выборки
tsne = TSNE(n_components=2, random_state=42)
cifar10_tsne_train = tsne.fit_transform(cifar10_data_train[:2000])
# t-SNE для тестовой выборки
# cifar10_tsne_test = tsne.transform(cifar10_data_test[:2000]) # Нельзя сделать такое предсказание
# UMAP для обучающей выборки
umap_model = UMAP(n_components=2, random_state=42)
cifar10_umap_train = umap_model.fit_transform(cifar10_data_train[:2000])
# UMAP для тестовой выборки
cifar10_umap_test = umap_model.transform(cifar10_data_test[:2000])
/usr/local/lib/python3.11/dist-packages/umap/umap_.py:1945: UserWarning: n_jobs value 1 overridden to 1 by setting random_state. Use no seed for parallelism.
warn(f"n_jobs value {self.n_jobs} overridden to 1 by setting random_state. Use no seed for parallelism.")
# Isomap для обучающей выборки
isomap = Isomap(n_components=2)
cifar10_isomap_train = isomap.fit_transform(cifar10_data_train[:2000])
# Isomap для тестовой выборки
cifar10_isomap_test = isomap.transform(cifar10_data_test[:2000])
# KernelPCA для обучающей выборки
kpca = KernelPCA(n_components=2, kernel='rbf', gamma=15)
cifar10_kpca_train = kpca.fit_transform(cifar10_data_train[:2000])
# KernelPCA для тестовой выборки
cifar10_kpca_test = kpca.transform(cifar10_data_test[:2000])
fig, axes = plt.subplots(2, 4, figsize=(20, 10))
# t-SNE
plot_2d_data(cifar10_tsne_train, cifar10_labels_train[:2000], 't-SNE Train', cmap='tab20', ax=axes[0, 0])
# plot_2d_data(cifar10_tsne_test, cifar10_labels_test[:2000], 't-SNE Test', cmap='tab20', ax=axes[1, 0]) # Нет такой функции, так как метод unsupervised
# UMAP
plot_2d_data(cifar10_umap_train, cifar10_labels_train[:2000], 'UMAP Train', cmap='tab20', ax=axes[0, 1])
plot_2d_data(cifar10_umap_test, cifar10_labels_test[:2000], 'UMAP Test', cmap='tab20', ax=axes[1, 1])
# Isomap
plot_2d_data(cifar10_isomap_train, cifar10_labels_train[:2000], 'Isomap Train', cmap='tab20', ax=axes[0, 2])
plot_2d_data(cifar10_isomap_test, cifar10_labels_test[:2000], 'Isomap Test', cmap='tab20', ax=axes[1, 2])
# KernelPCA
plot_2d_data(cifar10_kpca_train, cifar10_labels_train[:2000], 'KernelPCA Train', cmap='tab20', ax=axes[0, 3])
plot_2d_data(cifar10_kpca_test, cifar10_labels_test[:2000], 'KernelPCA Test', cmap='tab20', ax=axes[1, 3])
plt.tight_layout()
plt.show()
Опишите увиденное. Почему алгоритмы могли отработать не так, как вы ожидали?
**Ваш ответ здесь:** (o・・)ノ”(ノ<、):
transform, так как это непараметрический метод. Он не может применять обученную модель к новым данным.Сложная структура данных:
Неправильный выбор параметров:
perplexity для t-SNE).Стохастичность алгоритмов:
Перекрытие классов:
Методы снижения размерности, как и другие метрические методы испытывают трудности при работе с данными высокой размерности. Напишите как минимум две причины, почему.
**Ваш ответ здесь:** (o・・)ノ”(ノ<、):
Проклятие размерности
Вычислительная сложность
Один из способов решения этих проблем — перейти в другое, более репрезентативное пространство признаков, где объекты будут расположены в многообразии, которое легче представить в двумерном пространстве. Чтобы выполнить такое преобразование воспользуемся типичным подходом Transfer Learning — предобученными нейронными сетями. С помощью глубокой сети обученной на другом наборе изображений (ImageNet) мы перейдём в новое векторное пространство и затем применим методы снижения размерности.
Так как локальный подсчёт эмбеддингов изображений может занять много времени, Вы можете попробовать скачать их c помощью gdown:
gdown.download(id='16UgWo1Emt9ar1O4h2Xxed0ZpJZ0OG5V-', output='cifar10_deep_features.npy')
Downloading... From (original): https://drive.google.com/uc?id=16UgWo1Emt9ar1O4h2Xxed0ZpJZ0OG5V- From (redirected): https://drive.google.com/uc?id=16UgWo1Emt9ar1O4h2Xxed0ZpJZ0OG5V-&confirm=t&uuid=d1ef8eb2-f003-442e-97ed-9c29f21fab2b To: /content/cifar10_deep_features.npy 100%|██████████| 164M/164M [00:02<00:00, 68.4MB/s]
'cifar10_deep_features.npy'
FEATURES_PATH = './cifar10_deep_features.npy'
if not os.path.exists(FEATURES_PATH):
deep_cnn = InceptionV3(weights='imagenet', include_top=False, input_shape=(139, 139, 3))
cifar10_tensors_test = torch.nn.functional.interpolate(torch.tensor(
cifar10_images_test.transpose(0, 3, 1, 2)
), size=139).numpy().transpose(0, 2, 3, 1).astype(np.float32)
cifar10_tensors_train = torch.nn.functional.interpolate(torch.tensor(
cifar10_images_train.transpose(0, 3, 1, 2)
), size=139).numpy().transpose(0, 2, 3, 1).astype(np.float32)
cifar10_deep_features_test = deep_cnn.predict(
preprocess_input(cifar10_tensors_test)
).mean(axis=(1, 2)).reshape([cifar10_tensors_test.shape[0], -1])
cifar10_deep_features_train = deep_cnn.predict(
preprocess_input(cifar10_tensors_train)
).mean(axis=(1, 2)).reshape([cifar10_tensors_train.shape[0], -1])
np.save(FEATURES_PATH, [cifar10_deep_features_test, cifar10_deep_features_train])
else:
cifar10_deep_features_test, cifar10_deep_features_train = np.load(FEATURES_PATH, allow_pickle=True)
# Ваш код здесь:\(º □ º l|l)/
# t-SNE для обучающей выборки
tsne = TSNE(n_components=2, random_state=42)
cifar10_tsne_train = tsne.fit_transform(cifar10_deep_features_train[:2000])
# t-SNE для тестовой выборки
# cifar10_tsne_test = tsne.fit_transform(cifar10_deep_features_test[:2000])
# UMAP для обучающей выборки
umap_model = UMAP(n_components=2, random_state=42)
cifar10_umap_train = umap_model.fit_transform(cifar10_deep_features_train[:2000])
# UMAP для тестовой выборки
cifar10_umap_test = umap_model.transform(cifar10_deep_features_test[:2000])
/usr/local/lib/python3.11/dist-packages/umap/umap_.py:1945: UserWarning: n_jobs value 1 overridden to 1 by setting random_state. Use no seed for parallelism.
warn(f"n_jobs value {self.n_jobs} overridden to 1 by setting random_state. Use no seed for parallelism.")
# Isomap для обучающей выборки
isomap = Isomap(n_components=2)
cifar10_isomap_train = isomap.fit_transform(cifar10_deep_features_train[:2000])
# Isomap для тестовой выборки
cifar10_isomap_test = isomap.transform(cifar10_deep_features_test[:2000])
# KernelPCA для обучающей выборки
kpca = KernelPCA(n_components=2, kernel='rbf', gamma=15)
cifar10_kpca_train = kpca.fit_transform(cifar10_deep_features_train[:2000])
# KernelPCA для тестовой выборки
cifar10_kpca_test = kpca.transform(cifar10_deep_features_test[:2000])
fig, axes = plt.subplots(2, 4, figsize=(20, 10))
# t-SNE
plot_2d_data(cifar10_tsne_train, cifar10_labels_train[:2000], 't-SNE Train', cmap='tab20', ax=axes[0, 0])
# plot_2d_data(cifar10_tsne_test, cifar10_labels_test[:2000], 't-SNE Test', cmap='tab20', ax=axes[1, 0])
# UMAP
plot_2d_data(cifar10_umap_train, cifar10_labels_train[:2000], 'UMAP Train', cmap='tab20', ax=axes[0, 1])
plot_2d_data(cifar10_umap_test, cifar10_labels_test[:2000], 'UMAP Test', cmap='tab20', ax=axes[1, 1])
# Isomap
plot_2d_data(cifar10_isomap_train, cifar10_labels_train[:2000], 'Isomap Train', cmap='tab20', ax=axes[0, 2])
plot_2d_data(cifar10_isomap_test, cifar10_labels_test[:2000], 'Isomap Test', cmap='tab20', ax=axes[1, 2])
# KernelPCA
plot_2d_data(cifar10_kpca_train, cifar10_labels_train[:2000], 'KernelPCA Train', cmap='tab20', ax=axes[0, 3])
plot_2d_data(cifar10_kpca_test, cifar10_labels_test[:2000], 'KernelPCA Test', cmap='tab20', ax=axes[1, 3])
plt.tight_layout()
plt.show()